Systems and methods for pulse descriptor word generation using blind source separation

ABSTRACT

A method for generating pulse descriptor words (PDWs) including frequency and/or bandwidth data from time-varying signals received by a sensor includes filtering, at a plurality of blind source separation (BSS) modules, signals derived from the time-varying signals, each BSS module including a filtering subsystem having a plurality of filter modules. Each filter module has a frequency filter coefficient (α) and is parameterized by a center frequency (f). The method also includes transmitting at least one blind source separated signal from the BSS modules to a PDW generation module communicatively coupled to the filtering subsystem. The method further includes generating, using the PDW generation module and based on the blind source separated signal, at least one PDW parameter vector signal containing the frequency data. The method also includes updating, upon generating and based on the PDW parameter vector signal, values of α and/or f for each filter module.

BACKGROUND

The field of the disclosure relates generally to pulse descriptor word(PDW) vector signal processing, and, more specifically, to highperformance systems and methods for PDW generation using blind sourceseparation.

In known PDW vector signal processing systems and methods, fixedbandwidth channels are used to generate PDW vectors for deinterleavinginto constituent PDW data blocks (e.g., parameters). In at least someknown PDW vector signal processing systems, fixed bandwidth channelsreduce accuracy of estimates of resultant PDW parameters such asestimated values of center frequency, bandwidth, pulse time, and pulsewidth of signals received from a plurality of target signal emitters(e.g., radar signals). In order to improve speed and accuracy for usefulestimates of PDW parameter values, such fixed bandwidth channel-basedPDW vector signal processing systems require larger and more complexprocessor architectures. Further, even when size, weight, and cost arenot critical design constraints, at least some known systems and methodsfor PDW vector signal processing suffer from diminished efficiency andaccuracy in continuously generating high quality PDW parameter vectorssuitable for improved deinterleaving methods.

BRIEF DESCRIPTION

In one aspect, a method is provided for generating pulse descriptorwords (PDWs) including at least one of frequency data and bandwidthdata, from a plurality of time-varying signals received by a sensorcommunicatively coupled to a signal data processor. The method includesfiltering, at a plurality of blind source separation (BSS) modules ofthe signal data processor, signals derived from the plurality oftime-varying signals, each BSS module of the plurality of BSS modulesincluding a filtering subsystem having a plurality of filter modules,where each filter module of the plurality of filter modules has afrequency filter coefficient (α) and is parameterized by a centerfrequency (f). The method also includes transmitting at least one blindsource separated signal from the plurality of BSS modules to a PDWgeneration module communicatively coupled to the filtering subsystem.The method further includes generating, using the PDW generation moduleand based on the at least one blind source separated signal, at leastone PDW parameter vector signal containing the frequency data. Themethod also includes updating, upon generating the at least one PDWparameter vector signal, and based thereupon, at least one of a value ofα and a value of f for each filter module of the plurality of filtermodules.

In another aspect, a system is provided for processing a plurality oftime-varying signals to generate at least one PDW including at least oneof frequency data and bandwidth data. The system includes a sensorconfigured to receive the at least one time-varying signal, and a signaldata processor communicatively coupled to the sensor. The signal dataprocessor includes a plurality of BSS modules, each BSS module of theplurality of BSS modules having a filtering subsystem including aplurality of filter modules, where each filter module of the pluralityof filter modules has a frequency filter coefficient a and isparameterized by a center frequency f. The signal data processor alsoincludes a PDW generation module communicatively coupled to thefiltering subsystem. The plurality of BSS modules are configured tofilter signals derived from the plurality of time-varying signals andtransmit at least one blind source separated signal to the PDWgeneration module. The PDW generation module is configured to generate,based on the at least one blind source separated signal, at least onePDW parameter vector signal containing the frequency data to facilitateupdating, substantially simultaneously with generating the at least onePDW parameter vector signal, and based thereupon, at least one of avalue of α and a value of f for each filter module of the plurality offilter modules.

In yet another aspect, a signal data processor is provided forprocessing a plurality of time-varying signals to generate at least onePDW including at least one of frequency data and bandwidth data. Thesignal data processor includes a plurality of BSS modules, each BSSmodule of the plurality of BSS modules having a filtering subsystemincluding a plurality of filter modules, where each filter module of theplurality of filter modules has a frequency filter coefficient α and isparameterized by a center frequency f. The signal data processor alsoincludes a PDW generation module communicatively coupled to thefiltering subsystem. The plurality of BSS modules are configured tofilter signals derived from the plurality of time-varying signals andtransmit at least one blind source separated signal to the PDWgeneration module. The PDW generation module is configured to generate,based on the at least one blind source separated signal, at least onePDW parameter vector signal containing the frequency data to facilitateupdating, substantially simultaneously with generating the at least onePDW parameter vector signal, and based thereupon, at least one of avalue of α and a value of f for each filter module of the plurality offilter modules.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentdisclosure will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1 is a schematic diagram of an exemplary signal processing systemfor generating pulse descriptor words (PDWs) using blind sourceseparation (BSS).

FIG. 2 is a schematic diagram of an exemplary BSS channel that forms aportion of the signal processing system shown in FIG. 1.

FIG. 3 is a schematic diagram of an exemplary BSS state machine processthat may be used with the BSS channel state machine module shown in FIG.2.

FIG. 4A is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient alpha(α) determined during pre-training versus window size with multiplesignal-to-noise ratios (SNRs).

FIG. 4B is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting mean squared error (MSE)results for coefficient α for the graphical representation shown in FIG.4A versus window size.

FIG. 5A is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting frequency tracking resultsversus sample number for an SNR value of 20 dB.

FIG. 5B is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting MSE results for frequencytracking results for the graphical representation shown in FIG. 5Aversus sample number.

FIG. 6 is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting MSE results for frequencytracking for a range of SNRs.

FIG. 7A is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient α₁determined during pre-training versus window size with multiple SNRs.

FIG. 7B is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient α₂determined during pre-training versus window size with multiple SNRs.

FIG. 7C is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient α₃determined during pre-training versus window size with multiple SNRs.

FIG. 7D is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient β₁determined during pre-training versus window size with multiple SNRs.

FIG. 7E is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient β₂determined during pre-training versus window size with multiple SNRs.

FIG. 7F is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting values for coefficient β₃determined during pre-training versus window size with multiple SNRs.

FIG. 8A is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting MSE results for frequencyerror (Δf) determined during frequency tracking versus window size withmultiple SNRs.

FIG. 8B is a graphical representation of operation of the signalprocessing system shown in FIG. 1 depicting MSE results for bandwidtherror (Δw) determined during frequency tracking versus window size withmultiple SNRs.

FIG. 9 is a flowchart of an exemplary method of PDW generation using BSSthat may be used with the signal processing system shown in FIG. 1.

Unless otherwise indicated, the drawings provided herein are meant toillustrate features of implementations of this disclosure. Thesefeatures are believed to be applicable in a wide variety of systemscomprising one or more implementations of this disclosure. As such, thedrawings are not meant to include all conventional features known bythose of ordinary skill in the art to be required for the practice ofthe implementations disclosed herein.

DETAILED DESCRIPTION

In the following specification and the claims, reference will be made toa number of terms, which shall be defined to have the followingmeanings.

The singular forms “a”, “an”, and “the” include plural references unlessthe context clearly dictates otherwise.

“Optional” or “optionally” means that the subsequently described eventor circumstance may or may not occur, and that the description includesinstances where the event occurs and instances where it does not.

Approximating language, as used herein throughout the specification andclaims, may be applied to modify any quantitative representation thatcould permissibly vary without resulting in a change in the basicfunction to which it is related. Accordingly, a value modified by a termor terms, such as “about”, “approximately”, and “substantially”, are notto be limited to the precise value specified. In at least someinstances, the approximating language may correspond to the precision ofan instrument for measuring the value. Here and throughout thespecification and claims, range limitations may be combined and/orinterchanged, and such ranges are identified and include all thesub-ranges contained therein unless context or language indicatesotherwise.

As used herein, the terms “processor” and “computer” and related terms,e.g., “processing device”, “computing device”, and “controller” are notlimited to just those integrated circuits referred to in the art as acomputer, but broadly refers to a microcontroller, a microcomputer, aprogrammable logic controller (PLC), an application specific integratedcircuit (ASIC), and other programmable circuits, and these terms areused interchangeably herein. In the implementations described herein,memory may include, but is not limited to, a computer-readable medium,such as a random access memory (RAM), and a computer-readablenon-volatile medium, such as flash memory. Alternatively, a floppy disk,a compact disc-read only memory (CD-ROM), a magneto-optical disk (MOD),and/or a digital versatile disc (DVD) may also be used. Also, in theimplementations described herein, additional input channels may be, butare not limited to, computer peripherals associated with an operatorinterface such as a mouse and a keyboard. Alternatively, other computerperipherals may also be used that may include, for example, but not belimited to, a scanner. Furthermore, in the exemplary implementation,additional output channels may include, but not be limited to, anoperator interface monitor.

Furthermore, as used herein, the term “real-time” refers to at least oneof the time of occurrence of the associated events, the time ofmeasurement and collection of predetermined data, the time to processthe data, and the time of a system response to the events and theenvironment. In the implementations described herein, these activitiesand events occur substantially instantaneously.

The systems and methods described herein are directed to a signalprocessing system for generating pulse descriptor words (PDWs). Thesignal processing system detects a plurality of mixed signals (e.g.,radar signals) using a sensor. A signal data processor communicativelycoupled to the sensor uses blind source separation (BSS) and othersignal processing techniques to separate and identify one or moresignals of interest from the plurality of mixed signals. Signalprocessing techniques described herein include at least two filtermodules having distinct filter coefficients and parameterized by atleast one of frequency and bandwidth. The signal processing systemfurther updates and stores the filter coefficient and parameter of eachfilter module to enhance accuracy in identification and tracking ofsignal parameters (e.g., frequency, amplitude, etc.) of each identifiedsignal of interest.

The signal data processor uses BSS for PDW generation. In the systemsand methods described herein, BSS enables enhanced accuracy of PDWparameter estimations without relying on fixed bandwidth channels. Theimplementations described herein also facilitate faster and moreefficient PDW generation using less complex processing architecturesrelative to known fixed bandwidth channel-based systems. Theimplementations described herein further enable reduction of size,weight, and cost of high performance PDW signal processing systems andmethods. The systems and methods for PDW generation using blind sourceseparation described herein also provide continuous high speedgeneration of high signal quality PDW parameter vectors suitable forimproved deinterleaving methods.

FIG. 1 is a schematic diagram of an exemplary signal processing system100 for generating pulse descriptor words (PDWs) using BSS. Also knownas blind signal separation, BSS is used to separate (e.g., filter) oneor more source signals of interest from a plurality of mixed signals. Inapplications including, without limitation, an underdetermined case(e.g., fewer observed signals than signal sources), BSS facilitatesseparating and identifying pure signals of interest from an arbitraryset of time-varying signals (e.g., radar pulses from one or more signalemitters) without relying on substantial amounts of known informationabout the signal emitters, signals of interest, or the signal mixingprocess.

In the exemplary embodiment, signal processing system 100 includes asignal data processor 101 communicatively coupled to an antenna 102.Antenna 102, in the exemplary embodiment, is a wide-area sensor 103.Signal data processor 101 includes a pre-processor 104 and apost-processor 105. Sensor 103 is configured to receive signals fromradar signal emitters 106 and 107. Although two radar signal emitters106 and 107 are shown in FIG. 1, those of skill in the art willappreciate that sensor 103 may receive signals from any number of radarsignal emitters 106 and 107.

Sensor 103 is communicatively coupled to pre-processor 104 through apre-conditioner 108. In the exemplary embodiment, pre-conditioner 108includes a low noise amplifier 109, a band pass filter 110, and awideband analog-to-digital converter (ADC) 111. In operation,pre-conditioner 108 is configured to convert a sensor output signal 112received from sensor 103 into an incoming signal 113 transmitted topre-processor 104. Each incoming signal 113 is derived from atime-varying signal received at sensor 103. Time-varying signal mayinclude a mix of signals received from radar signal emitters 106 and107. For example, time-varying signals may include a first radar signal114 and a second radar signal 116.

In the exemplary embodiment, pre-processor 104 includes one or moresignal denoising modules 118, and a plurality of blind source separation(BSS) modules 120. Each BSS module 120 is coupled to a single signaldenoising module 118, and represents one BSS channel. A total number ofBSS channels in signal processing system 100 is expressed as K. Signaldenoising module 118 transmits a denoised signal 124 and a state energysignal 126 to each respective BSS module 120 (e.g., 120 a, 120 b, . . ., 120K) of the plurality of BSS modules 120. State energy signal 126represents a quantity (e.g., an analog voltage level) that isproportional to an amplitude of incoming signal 113 at particularsampled time points (e.g., states).

In operation, incoming signal 113 is transmitted from pre-conditioner108 to signal denoising module 118 where incoming signal 113 undergoessignal denoising and is subsequently transmitted as denoised signal 124to the each BSS module 120. For example, first radar signal 114 isinitially received at sensor 103 as a pulse having signalcharacteristics including, without limitation, a frequency and abandwidth. In this example, a single pulse of first radar signal 114,after processing by pre-conditioner 108, is then received at signaldenoising module 118 as a mixed signal (e.g., the incoming signal 113represents a signal pulse of the first radar signal 114 and has variouscharacteristics including, without limitation, noise and informationother than the desired information of interest). Signal denoising module118 denoises the mixed incoming signal 113 prior to transmittingdenoised signal 124 having a frequency and a bandwidth (or a regularpattern of frequencies and bandwidths) to the BSS modules 120. Methodsimplemented by signal processing system 100 are performed insubstantially real time by the devices and systems described above, andas shown and described below in further detail with reference to FIG. 2.

Further, in the exemplary embodiment, pre-processor 104 includes one ormore PDW generation modules 128 coupled to each BSS module 120, and apulse denoising module 130 coupled to each BSS module 120. PDWgeneration module 128 generates PDW parameter vector signals 138 basedon blind source separated signals 129 received from each BSS module 120.Each PDW parameter vector signal 138 contains data representative ofcharacteristics of interest of one of radar signals 114 and 116 derivedfrom a singular pulse of blind source separated signal 129 (e.g.,frequency, bandwidth, time of arrival, time of departure, pulse width,pulse amplitude, pulse repetition interval, and/or angle of arrival(AOA)). Pulse denoising module 130 also generates an unknown signalstate space representation signal 139 based on blind source separatedsignals 129. Unknown signal state space representation signal 139contains data representative of additional (e.g., non-PDW-type)characteristics of interest of one of radar signals 114 and 116 fromwhich usable spatial information about one of radar signal emitters 106and 107 is discernable. PDW parameter vector signals 138 and unknownsignal state space representation signals 139 are transmitted topost-processor 105. Signal denoising module 118, PDW generation module128, and pulse denoising module 130 include suitable signal filtering,signal amplification, signal modulation, signal separation, signalconditioning, and/or ADC circuitry implemented using analog and/ordigital electronic circuit components. Also, in the exemplaryembodiment, each BSS module 120 transmits a respective blind sourceseparated signal 129 (e.g., 129 a, 129 b, . . . , 129K) to PDWgeneration module 128 and to pulse denoising module 130.

Post-processor 105 includes a computing device 132 that includes amemory 134. As described above, PDW generation module 128 receives blindsource separated signals 129 from each respective BSS module 120. PDWgeneration module 128 then utilizes the blind source separated signals129 to generate a PDW parameter vector signal 138, which is subsequentlytransmitted to post-processor 105. PDW parameter vector signal 138 isreceived by computing device 132 and stored as computer-readable data inmemory 134 including, without limitation, as at least one buffered dataset. Pulse denoising module 130 is also configured to receive blindsource separated signals 129 from each respective BSS module 120. Pulsedenoising module 130 is further configured to utilize the blind sourceseparated signals 129 to generate the unknown signal state spacerepresentation signal 139, which is subsequently transmitted topost-processor 105. Unknown signal state space representation signal 139is received by computing device 132 and stored as computer-readable datain memory 134 including, without limitation, as at least one buffereddata set. In the exemplary embodiment, computing device 132 fetchesbuffered data sets from memory 134 for processing using a computer-basedmethod employing an operating system running software executed frominstruction set data also stored in memory 134 (e.g., from one or morecomputer-readable storage media).

Computing device 132 implements a computer-based method (e.g., fromsoftware instructions stored in one or more computer-readable storagemedia including, without limitation, in memory 134) to carry outoperations based on data contained in at least one of PDW parametervector signal 138 and unknown signal state space representation signal139. Such operations include, without limitation, detecting, processing,quantifying, storing, and displaying (e.g., in human readable data form)various characteristics of at least one radar signal (e.g., signals 114and 116) represented as data in at least one of PDW parameter vectorsignal 138 and unknown signal state space representation signal 139. Forexample, PDW parameter vector signal 138 generated by PDW generationmodule 128 contains a plurality of PDW vector data blocks structured ina vector form, where each PDW vector data block contains one parameterof first radar signal 114. Parameters (e.g., representative of at leastone characteristic of first radar signal 114) include, withoutlimitation, frequency, bandwidth, time of arrival, time of departure,pulse width, pulse amplitude, pulse repetition interval, and/or AOA.Computing device 132 reads PDW parameter vector signal 138 and carriesout at least one of the aforementioned operations on at least one PDWvector data block of the plurality of PDW vector data blocks. Also, inthe exemplary embodiment, computing device 132 reads and separates(e.g., deinterleaves) PDW parameter vector signal 138 into itsconstituent PDW vector data blocks, and stores fewer PDW vector datablocks in memory 134 than the total number of PDW vector data blockscontained in PDW parameter vector signal 138. Deinterleaving of PDWparameter vector signal 138 enables determining characteristics ofinterest of radar signals 114 and/or 116 by computing device 132 to, forexample, and without limitation, accurately determine and track spatialinformation for radar signal emitters 106 and/or 107. In otherimplementations, computing device 132 reads and separates all PDW vectordata blocks from one another and stores all data contained therein inmemory 134. Computing device 132 performs the aforementioned operationssubstantially simultaneously (e.g., in real time) upon receipt of radarsignals 114 and 116 by sensor 103.

Resultant data from operations performed by computing device 132 arestored in memory 134. Further, in the exemplary embodiment, computingdevice 132 causes post-processor 105 to transmit a data output signal142 to a human machine interface (HMI) to facilitate at least one of aninteraction, a modification, a visualization, at least one furtheroperation, and a viewable recording of information about radar signals114 and 116 by a user of signal processing system 100. HMI is, forexample, a display 144 which receives data output signal 142 frompost-processor 105. In one example, characteristics (e.g., locationcharacteristics such as grid coordinates in a physical spatial domain)representing a physical location of radar signal emitters 106 and 107,as determined by signal processing system 100, are displayed on display144, and are updated in substantially in real time. Data output signal142 is also transmitted from post-processor 105 to at least one deviceand/or system (e.g., a vehicle 146) associated with signal processingsystem 100. Further, computing device 132 enables post-processor 105 totransmit, in substantially real time, an actuator control signal 148 toan actuator controller 150 included within vehicle 146 to facilitatecontrolling vehicle 146. For example, vehicle 146 may be a remotelyand/or autonomously operated land vehicle and/or an unmanned aerialvehicle (UAV).

In one mode of operation, at least one of frequency and bandwidthinformation contained in respective PDW parameter vector signals 138 isdisplayed on display 144 along with locations of respective radar signalemitters 106 and 107 to facilitate accurate tracking of locations andassociation with particular radar signal emitters 106 and 107. In caseswhere at least one radar signal emitter 106 and 107 is mobile, display144 is automatically updated in substantially real-time to show thelocation information of at least one respective mobile radar signalemitter 106 and 107. Further, computing device 132 also determines atleast one of a velocity, an acceleration, a trajectory, and a track(e.g., including present and prior locations) of the at least onerespective mobile radar signal emitter 106 and 107. In another mode ofoperation, characteristics determined by signal data processor 101 alsotrigger a variety of substantially real time physical actions inphysical devices and systems in communication with signal processingsystem 100. For example, characteristics of radar signal emitters 106and 107, including frequency and bandwidth determined by signalprocessing system 100, are transmitted in substantially real-time asdata to actuator controller 150 in vehicle 146 (e.g., to control ruddersand flaps of a UAV). If radar signal emitters 106 and 107 areunauthorized (e.g., hostile, previously undetected, etc.) radar signalemitters determined to be a threat, actuator controller 150 maneuversvehicle 146 to avoid an area of operation of signal emitters 106 and 107or engages signal emitters 106 and 107. As a further example,characteristics of radar signal emitters 106 and 107 determined bysignal data processing methods described herein are transmitted insubstantially real time in a control signal to at least one of anelectronic support measure (ESM) device and an electronic warfare (EW)system associated with signal processing system 100 to direct, forexample, a radar jamming signal at radar signal emitters 106 and 107operating in the surveillable environment of sensor 103 withoutauthorization.

In operation, each BSS module 120 of the plurality of BSS modules 120 insignal processing system 100 implements filtering methods with dynamicupdating to enable generating high quality PDWs containing at least oneof frequency, center frequency, bandwidth, pulse time, and pulse widthinformation. BSS modules 120 may have a pipelined and parallelizedarchitecture in some embodiments. Such improved accuracy and resolutionof PDWs to track, for example, frequency and bandwidth of radar signalsof interest facilitates identifying, determining, and/or analyzing radarsignal emitters 106 and 107 from which associated radar signals areemitted. For example, information including, without limitation,information derived from PDWs from radar signal emitters 106 and 107 isdisplayed on display 144 after being transmitted thereto bypost-processor 105 as data output signal 142, as described above. Thisimproved information enables signal processing system 100 to distinguishfirst radar signal emitter 106 from second radar signal emitter 107.Also, for example, different radar signal emitters (e.g., first radarsignal emitter 106 and second radar signal emitter 107) in a surveilledenvironment of sensor 103 are plotted at respective locations (e.g.,grid coordinates) on display 144 (e.g., as a map).

Also, in operation, the plurality of BSS modules 120 separate aplurality of denoised signals 124. As further shown and described belowwith reference to FIGS. 2 and 3, each BSS module 120 contains aplurality of tunable filters, where each filter operates based on filterparameters including, without limitation, a center frequency and abandwidth. Further, in the exemplary embodiment, pre-processor 104includes a BSS control module 196, which facilitates controlling eachrespective BSS module 120 of the plurality of BSS modules 120. BSScontrol module 196 receives respective BSS data signals 197 (e.g., 197a, 197 b, . . . , 197K) containing BSS-related information including,without limitation, frequency, bandwidth, and state, from each BSSmodule 120 of the plurality of BSS modules 120. Based on the BSS-relatedinformation contained in BSS data signals 197, BSS control module 196also generates and transmits respective BSS control signals 198 (e.g.,198 a, 198 b, . . . , 198K) back to each respective BSS module 120 tocontrol, for example and without limitation, a timing of receipt ofdenoised signal 124 and transmission of respective blind sourceseparated signals 129 to at least one of PDW generation module 128 andpulse denoising module 130. Information contained in BSS data signals197 and BSS control signals 198 is used by BSS control module 196 tofacilitate implementation of a feedback control loop.

FIG. 2 is a schematic diagram of an exemplary BSS channel 200 (e.g., BSSmodule 120 a receiving denoised signal 124 from signal denoising module118) that forms a portion of the signal processing system 100 shown inFIG. 1. As described above, signal denoising module 118 transmitsdenoised signal 124 and state energy signal 126. Also, in the exemplaryembodiment, state energy signal 126 is embodied in a plurality of stateenergy signals 126. Each state energy signal 126 of the plurality ofstate energy signals 126 contains information that is representative ofthe state (e.g., the analog voltage level that is proportional to theamplitude of incoming signal 113 at particular sampled time points) of arespective state output 202 of signal denoising module 118. Theplurality of state energy signals 126 are received by a state energyanalysis subsystem 204. State energy analysis subsystem 204 determines acenter frequency (e.g., f₀) of respective state energy signals 126 of Ssignals (e.g., 126 a, 126 b, . . . , 126S) corresponding to S filterstates of a filtering subsystem 207. State energy analysis subsystem 204includes a window summer module 206 configured to determine a totalenergy within a set of S windows of length N_(e) (e.g., one for eachstate of a BSS channel state machine module 208 of BSS module 120a). BSSchannel state machine module 208 coordinates a timing of filtering ofdenoised signal 124 by filtering subsystem 207. State energy analysissubsystem 204 also includes a maximum energy detection module 210coupled to window summer module 206. Maximum energy detection module 210is configured to receive S summed window signals 212 (e.g., 212 a, 212b, . . . , 212S) and determine a maximum energy of each summed windowsignal 212 of the S summed window signals 212. Maximum energy detectionmodule 210 is further configured to determine and transmit an initialfrequency signal 214 to a signal frequency and bandwidth tracker module216 coupled to maximum energy detection module 210.

In an exemplary embodiment, initial frequency signal 214 isrepresentative of the f₀ of the maximum energy of the respective stateenergy signal 126 corresponding to the associated state of BSS channel200. Signal frequency and bandwidth tracker module 216 uses initialfrequency signal 214 to determine a center frequency (“Cf”) and abandwidth (“BW”) of the respective summed window signal 212corresponding to the maximum energy state of BSS channel 200. Signalfrequency and bandwidth tracker module 216 further outputs a Cf and BWsignal 218 to BSS channel state machine module 208. BSS channel statemachine module 208 is coupled to filtering subsystem 207, signalfrequency and bandwidth tracker module 216, an input buffer module 220,and computing device 132. Substantially simultaneously with receipt ofCf and BW signal 218 by BSS channel state machine module 208 from signalfrequency and bandwidth tracker module 216, input buffer module 220delays filtering of denoised signal 124 by filtering subsystem 207 toenable BSS channel state machine 208 to update Cf and BW filterparameters of filtering subsystem 207 (as further described below).

In the exemplary embodiment, filtering subsystem 207 is a tunable filterbank including a plurality of filter modules including, for example, andwithout limitation, a low filter (“F_(lo)”) module 207 a, a main filter(“F”) module 207 b, and a high filter (“F_(hi)”) module 207 c. In otherimplementations (e.g., as shown and described below with reference toFIG. 5), filtering subsystem 207 includes greater than or less thanthree filter modules. Input buffer module 220 is coupled to and betweenfiltering subsystem 207 and signal denoising module 118, and isconfigured to transmit a plurality of filter input signals 228 (e.g.,228 a, 228 b, and 228 c) to respective filter modules (e.g., 207 a, 207b, and 207 c) in filtering subsystem 207. Input buffer module 220 isfurther configured to receive a delay signal 227 transmitted from afirst output of BSS channel state machine module 208. Delay signal 227dictates a timing of outputting filter input signal 228 to filteringsubsystem 207. From a second output, BSS channel state machine module208 transmits a center frequency and bandwidth update signal 232 tofiltering subsystem 207. Center frequency and bandwidth update signal232 enables continuous updating of Cf and BW operational parameters andassociated filter coefficients a (“alpha”) and β (“beta”), respectively,of each filter module (e.g., 207 a, 207 b, and 207 c) in filteringsubsystem 207. Center frequency and bandwidth update signal 232 thusfacilitates accurate tracking of denoised signal 124 frequency andbandwidth to yield a continuous and undistorted blind source separatedsignal 129 a output from BSS module 120 a and BSS channel 200.

In the exemplary embodiment, filtering subsystem 207 uses digital and/oranalog electronic circuitry including, without limitation, circuitsinstantiated in at least one of a field-programmable gate array (FPGA)and an application-specific integrated circuit (ASIC). Also, in theexemplary embodiment, at least a portion of the methods implemented inBSS channel 200 are instantiated via software on at least one of ageneral purpose processor (e.g., computing device 132) and a digitalsignal processor (DSP). Further, in the exemplary embodiment,operational parameters of each filter module (e.g., 207 a, 207 b, and207 c) in filtering subsystem 207 are stored in memory 134, and areupdated substantially simultaneously (e.g., in real time) withtransmission of center frequency and bandwidth update signal 232 by BSSchannel state machine module 208.

In the exemplary embodiment, filter module F_(lo) 207 a, filter module F207 b, and filter module F_(hi) 207 c receive respective filter inputsignals (e.g., 228 a, 228 b, and 228 c) from input buffer module 220,and are each further coupled to BSS channel state machine module 208.Filtering subsystem 207 is further configured to transmit a plurality ofsignal energy signals 234, where filter modules F_(lo) 207 a, F 207 b,and F_(hi) 207 c each transmit respective signal energy signals (e.g.,234 a, 234 b, and 234 c, respectively) to BSS channel state machinemodule 208. Further, in the exemplary embodiment, filter module F 207 balso transmits signal energy signal 234 b as the respective blind sourceseparated signal 129 a transmitted from BSS module 120 a to PDWgeneration module 128 and to pulse denoising module 130 for furtherprocessing (e.g., deinterleaving of PDW parameter vector signal 138 bycomputing device 132, as shown and described above with reference toFIG. 1). Information contained in the plurality of signal energy signals234 is used by BSS channel state machine module 208 for generating andtransmitting center frequency and bandwidth update signal 232 tofiltering subsystem 207 (as further shown and described below withreference to FIGS. 3 and 4).

In operation, feedback in BSS channel 200 is used to determine where(e.g., at what value or values) to place the Cf and BW of each filtermodule (e.g., filter modules F_(lo) 207 a, F 207 b, and F_(hi) 207 c) offiltering subsystem 207 over all time. The feedback includes acquiringenergy measurements resulting from existing filter settings (e.g., fromsignal energy signals 234 a, 234 b, and 234 c), and continuously andadaptively updating respective filter parameters Cf and BW and filtercoefficients a and β, while maintaining as complete a coverage in timeand frequency as possible. Subsequent pulses of radar signals arefiltered by filtering subsystem 207 with filter modules F_(lo) 207 a, F207 b, and F_(hi) 207 c having respective filter parameters andcoefficients tuned to enable filtering subsystem 207 to multitask in avery efficient manner (e.g., under control, at least in part, of BSScontrol module 196, as described above with reference to FIG. 1).

Also, in operation, signal frequency and bandwidth tracker module 216includes a tracking algorithm to track a value of the initial frequencysignal 214. Specifically, the Cf of initial frequency signal 214 changesat any rate up to a maximum predetermined rate set by the trackingalgorithm (e.g., determined by at least one of computing device 132, BSSchannel state machine module 208, and BSS control module 196). A trackwindow of the tracking algorithm is short enough to support a chirprate, but long enough to handle the signal noise level. In particular,the tracking algorithm is robustly implemented by BSS channel 200including, without limitation, in conjunction with computing device 132,as a function of all of the following: parameter and/or coefficientsettings of the plurality of filter modules (e.g., 207 a, 207 b, and 207c), noise levels, signal frequency change characteristics, amplitudedifferences, and ability to pull-in signals within range required bysignal denoising module 118. For example, and without limitation, wheresignal denoising module 118 has twenty states (e.g., S=20) with a 1 GHzbandwidth, BSS channel 200 tracks radar signals with a frequency offsetfrom an initial frequency (e.g., pull-in range) up to ±25 MHz (e.g.,0.025 GHz).

In the exemplary embodiment, each filter module (e.g., 207 a, 207 b, and207 c) in filtering subsystem 207 is an infinite impulse response (IIR)filter. Also, in the exemplary embodiment, BSS channel 200 processesradar signals rather than communications signals and, therefore, theeffects of a non-constant group delay caused by using IIR filters isless important than with communications signals. IIR filters adequatelymeet the signal quality required for post-filtering PDW deinterleavingby post-processor 105.

Filter module F 207 b is used as the primary filter for separatingfilter input signal 228 b derived from denoised signal 124. Filtering offilter input signals 228 a and 228 c by filter modules F_(lo) 207 a andF_(hi) 207 c, respectively, is used in the tracking process to keepfilter module F 207 b relatively accurate in determining both frequencyand bandwidth. Also, in the exemplary embodiment, filter modules F_(lo)207 a and F_(hi) 207 c are offset by fixed amounts in frequency andbandwidth and, as with filter module F 207 b, are continuously monitoredto facilitate appropriate and timely tuning of Cf and BW.

Each of the filter modules F_(lo) 207 a, F 207 b, and F_(hi) 207 c areparameterized by two values (e.g., Cf and BW). In an alternativeimplementation, not shown, filtering subsystem 207 includes two filtermodules (e.g., filter modules F 207 b and F_(hi) 207 c), rather thanthree filter modules, BSS channel 200 has a fixed BW, and a simplifiedtracking process tracks only frequency. In this simplified case, Cf andBW of filter module F 207 b are referred to as f and w, respectively,such that:

center frequency(F _(hi))=f+Δf   Equation 1

bandwidth(F _(hi))=w   Equation 2

For the exemplary embodiment, where filtering subsystem 207 includesthree filter modules (e.g., filter modules F_(lo) 207 a, F 207 b, andF_(hi) 207 c), Cf and BW of filter module F 207 b are defined accordingto Equations 1 and 2, and Cf and BW (e.g., f and w, respectively) offilter modules F_(lo) 207 a and F_(hi) 207 c are defined as follows:

center frequency(F _(lo))=f−Δf   Equation 3

bandwidth(F _(lo))=w−Δw   Equation 4

center frequency(F _(hi))=f+2Δf   Equation 5

bandwidth(F _(hi))=w+2Δw   Equation 6

Also, in operation, respective signal energy signals 234 (e.g., 234 a,234 b, and 234 c) output by respective filter modules (e.g., filtermodules F_(lo) 207 a, F 207 b, and F_(hi) 207 c) in filtering subsystem207 have their output energies determined by BSS channel state machinemodule 208 including, without limitation, in conjunction with methodsperformed using at least one of computing device 132 and BSS controlmodule 196. For real-valued signal energy signals 234, the outputenergies are determined through squaring, and for complex-valued signalenergy signals 234, the output energies are determined by taking theabsolute value. For either real-valued or complex-valued signal energysignals 234, determination of the output energies in the case offiltering subsystem 207 having three filter modules (e.g., F_(lo) 207 a,F 207 b, and F_(hi) 207 c) results in a sequence of energy measurementtriples (E(n), E_(lo)(n), E_(hi)(n)), n=1,2, . . . ), where n representsthe state of BSS channel 200, as described above. In the simplified twofilter case, determination of the output energies of signal energysignals 234 results in a sequence of energy measurement pairs (E(n),E_(hi)(n)), n=1,2, . . . ), and facilitates the following updates to theCf (e.g., f) parameters of filter modules F 207 b and F_(hi) 207 c:

f←f+α ₀*[(E(n)−E _(hi)(n))/(E(n)+E _(hi)(n))]+α₁   Equation 7

In the exemplary embodiment where filtering subsystem 207 includes threefilter modules (e.g., F_(lo) 207 a, F 207 b, and F_(hi) 207 c), f and wparameters are updated as follows:

f←f|α ₀*[(E(n)−E _(lo)(n))/(E(n)+E _(lo)(n))]+α₁*[(E(n)−E_(hi)(n))/(E(n)+E _(hi)(n))]+α₂   Equation 8

w←w+β ₀ *[E(n)−E _(lo)(n)]/[E(n)+E _(lo)(n)]+β₁*[(E(n)−E_(hi)(n))/(E(n)+E _(hi)(n))]+β₂   Equation 9

where initial values of coefficient vectors α and β are determined andstored in memory 134 during a pre-training process (e.g., implemented byat least one of computing device 132, BSS channel state machine module208, and BSS control module 196), and are functions of window size, BW,and signal-to-noise ratio (SNR). Initial values of α and β aredetermined from at least one of an initial denoised signal 124 and aninitial state energy signal 126 received at BSS channels 200.

Referring again to FIG. 2, in operation of the exemplary embodiment,respective filter input signals (e.g., 228 a, 228 b, and 228 c) derivedfrom at denoised signal 124 are provided substantially simultaneously toeach filter module (e.g., F_(lo) 207 a, F 207 b, and F_(hi) 207 c) infiltering subsystem 207 of each BSS module 120 of the plurality of BSSmodules 120 in signal processing system 100. In BSS channel 200, forexample, the resulting blind source separated signal 129 a output byfiltering subsystem 207 is further vectorized into PDW parameter vectorsignal 138 by PDW generation module 128 to further facilitate accuratetracking and determination of frequency and/or bandwidth of at least oneradar signal. Therefore, BSS channel 200 enables signal processingsystem 100 to implement high performance real time tracking of aplurality of time-varying radar signals streaming through pre-processor104.

The aforementioned filtering methods enable signal processing system 100to generate high quality PDW parameter vector signals 138 that are usedfor identifying, determining, and analyzing radar signal emitters 106and 107. For example, PDW parameter vector signals 138 associated withradar signal emitter 106 are displayed on display 144, as describedabove. Also, for example, improved information about frequencies and/orbandwidths contained in at least two PDW parameter vector signals 138enable signal processing system 100 to distinguish first radar signalemitter 106 from second radar signal emitter 107. These radar signalemitters 106 and 107 are plotted at respective locations on display 144(e.g., as a map).

FIG. 3 is a schematic diagram of an exemplary BSS state machine process300 that may be used with the BSS channel state machine module 208 shownin FIG. 2. In the exemplary implementation, BSS state machine process300 includes a plurality of states 302. The plurality of states 302includes a first state 304, a second state 306, a third state 308, afourth state 310, a fifth state 312, and a sixth state 314. Also, in theexemplary embodiment, BSS state machine process 300 (including, withoutlimitation, performed in conjunction with at least one of computingdevice 132 and BSS control module 196) moves through the plurality ofstates 302 as follows: first state 304→second state 306→third state308→fourth state 310→fifth state 312→sixth state 314→second state 306.First state 304 includes initialization of state energy buffers, and itbegins upon a user powering on signal processing system 100. In order tocompare energies of different states, a continuous sum is determinedover a time window of length N_(e). Thus, first state 304 enables theinitial sum to be determined upon system power-up and is neverreentered.

Also, in the exemplary implementation, second state 306 includesinitialization of the signal frequency. Once each state's summed energyis computed, a maximum value thereof is determined in S clocks and aninitial tracking frequency f₀ is determined using a linear relationshipbetween the states and their corresponding frequencies. Second state 306also includes initiation of the tracking frequency that is input to thetunable tracking filters of filtering subsystem 207 (shown in FIG. 2),offset appropriately. Further, in the exemplary implementation, thirdstate 308 includes initialization of filter output buffers. In order tocompare filter output energies from all the tracking filters offiltering subsystem 207 over a time window of length N_(f) with theinitial frequency setting, third state 308 waits N_(f) sample times sothat the summed energies accurately reflect the effects of the frequencythat is set.

Further, in the exemplary implementation, fourth state 310 includessearching the delayed signal. After obtaining accurate filter outputenergies, the frequency and bandwidth updates are computed correctly.Thus, fourth state 310 also includes initiating the tracking loop. To doso, fourth state 310 further includes switching to a delayed sample fromthe sample buffer of length N_(s) and attempts to pull-in the signaluntil a signal presence indicator is equal to or greater than apre-determined threshold. If the signal presence indicator is not equalto or greater than the pre-determined threshold, fourth state 310transitions back to second state 306 after a search counter expires.

Furthermore, in the exemplary implementation, fifth state 312 includestracking the delayed signal. After the signal is detected, it iscontinually tracked from the delay sample buffer as long as the signalis present, or until a track timeout occurs. The track timeoutfacilitates preventing the tracking filter resources in filteringsubsystem 207 from being kept busy by long communications signals (e.g.,which would prevent those filtering resources from being utilized formore important radar signals). A track timeout event during fifth state312 causes fifth state 312 to transition back to second state 306.However, if the signal presence indicator is equal to or less than thepre-determined threshold, fifth state 312 transitions to sixth state314. Moreover, in the exemplary implementation, sixth state 314 includesholding the delayed signal. When the tracked signal is no longer present(e.g., no longer detected by sensor 103), the hold state of sixth state314 enables preventing the frequency from being updated, and signals BSSstate machine process 300 to start a hold timer. If the signal presenceindicator is equal to or greater than the pre-determined threshold,sixth state 314 transitions back to tracking the delayed signal (e.g.,fifth state 312). Otherwise, the hold timer expires and sixth state 314transitions back to second state 306.

FIG. 4A is a graphical representation (e.g., graph 400) of operation ofthe signal processing system 100 shown in FIG. 1 depicting values forcoefficient alpha (α) determined during pre-training versus window sizewith multiple SNRs. FIG. 4B is a graphical representation (e.g., graph402) of operation of the signal processing system 100 shown in FIG. 1depicting mean squared error (MSE) results for coefficient α for graph400 versus window size. In the exemplary implementation, graph 400 plotsresults for coefficient a (y-axis) determined at five different SNRsusing the systems and methods described above with reference to FIGS.1-3. Results of α are also plotted in graph 400 over window sizes of 100to 16400 on the x-axis. Graph 400 includes a first plot 404 ofdetermined a values at an SNR of 15 decibels (dB). Graph 400 alsoincludes a second plot 406 and a third plot 408 of determined a valuesat SNRs of 20 dB and 25 dB, respectively. Graph 400 further includes afourth plot 410 and a fifth plot 412 of determined α values at SNRs of30 dB and 100 dB, respectively. Also, first plot 404, second plot 406,third plot 408, fourth plot 410, and fifth plot 412 are substantiallyequal in graph 400 and all substantially overlap, indicating thatdetermined values of α are dependent on window size between window sizesvalues of 100 and approximately 4000. At windows size values between4000 and 16400, on the other hand, determined α values are independentof window size in graph 400. The aforementioned dependency relationshipbetween determined a values and window sizes also holds for the fiveabove-listed SNRs in first plot 404, second plot 406, third plot 408,fourth plot 410, and fifth plot 412 in graph 400, indicating that thesystems and methods shown and described above with reference to FIGS.1-3 are implementable with substantially similar benefits in operationof the exemplary implementation on hardware and processing architectureshaving varying SNRs depending on particular applications of signalprocessing system 100.

Further, in the exemplary implementation, graph 402 plots results forMSE of coefficient a (y-axis) determined at the same five SNRs as inFIG. 4A. Results of MSE of a are also plotted in graph 402 over the samewindow sizes as in FIG. 4A. Graph 402 includes a sixth plot 414 ofdetermined MSE of α values at an SNR of 15 decibels (dB). Graph 402 alsoincludes a seventh plot 416 and an eighth plot 418 of determined MSE ofα values at SNRs of 20 dB and 25 dB, respectively. Graph 402 furtherincludes a ninth plot 420 and a tenth plot 422 of determined MSE of αvalues at SNRs of 30 dB and 100 dB, respectively. Also, in the exemplaryimplementation, between window size values of 4000 and 16400 in graph402, sixth plot 414, seventh plot 416, eighth plot 418, ninth plot 420,and tenth plot 422 are substantially similar, with a greatest variationof approximately 0.3*10⁻⁵ in determined MSE of α values occurringbetween sixth plot 414 (15 dB SNR) and tenth plot 422 (100 dB SNR) at awindow size of approximately 4200. Between window size values of 100 and4000 in graph 402, the greatest variation of approximately 2.7*10⁻⁵ indetermined MSE of α values occurs between sixth plot 414 (15 dB SNR) andtenth plot 422 (100 dB SNR) at a window size of approximately 300.Overall, in graph 402, determined MSE of α values vary with lessermagnitudes as SNR increases. Between window size values of 4000 and16400, however, MSE of α values exhibit diminishingly small variationsacross all five SNRs, indicating (as in FIG. 4A) that the systems andmethods shown and described above with reference to FIGS. 1-3 areimplementable with substantially similar benefits in operation of theexemplary implementation on hardware and processing architectures havingvarying SNRs depending on particular applications of signal processingsystem 100.

FIG. 5A is a graphical representation (e.g., graph 500) of operation ofthe signal processing system 100 shown in FIG. 1 depicting frequencytracking results versus sample number for an SNR value of 20 dB. FIG. 5Bis a graphical representation (e.g., graph 502) of operation of thesignal processing system 100 shown in FIG. 1 depicting MSE results forfrequency tracking results for the graphical representation shown inFIG. 5A versus sample number. Graph 500 includes a first plot 504 ofactual frequencies in gigahertz (GHz) on the y-axis (e.g., randomlyselected pulses of radar signals of known frequency received and sampledby sensor 103 of signal processing system 100) over sample numbers from0 (zero) to 1024 on the x-axis. Graph 500 also includes a second plot506 of frequency (GHz) values determined (e.g., as PDW data blockscontained in deinterleaved PDWs derived from blind source separation andfiltering, as shown and described above with reference to FIGS. 1-2)over sample numbers 0 to 1024. Also, first plot 504 and second plot 506are substantially equal in graph 500, indicating that, at SNR=20 dB,signal processing system 100 efficiently generates PDWs containinghighly accurate frequency information derived from blind sourceseparated and filter signals.

Further, graph 502 plots results for MSE for the frequency trackingresults over sample numbers 0 to 1024 shown and described above withreference to FIG. 5A. Graph 502 includes a third plot 508 of determinedMSE of frequency (Hz*10⁻³) at an SNR of 20 decibels (dB). In graph 502,MSE of frequency values vary by no more than about 1*10⁻³ Hz over samplenumbers 0 to 1024, and no particular subset of sample numbers exhibitssubstantially more variation than another particular subset of samplenumbers, indicating accurate, precise, and consistent high performancetracking of actual frequencies by signal processing system 100 over arange of about 0.23 GHz to 0.3 GHz.

FIG. 6 is a graphical representation (e.g., graph 600) of operation ofthe signal processing system 100 shown in FIG. 1 depicting MSE resultsfor frequency tracking for a range of SNRs. Graph 600 includes a plot602 of determined MSE (y-axis) of frequency in Hertz (Hz) for SNRs(y-axis) ranging from −20 dB to 20 dB (e.g., frequency trackingperformance as a function of SNR for signal processing system 100).Operational data of signal processing system 100 plotted in graph 600was obtained in substantially the same manner as for FIGS. 5A and 5Bover sample numbers 0 to 1024 and with a maximum chirp rate of 3815 GHzper second. MSE values in graph 600 decline from a maximum of about 10⁴Hz at an SNR value of −20 dB to approximately 200 Hz at an SNR of 0 dB,and exhibit substantially the same downward trend in MSE for frequencytracking with increasing SNR values as do MSE of a values as shown anddescribed above with reference to FIG. 4B. For SNR values greater thanor equal to −20 dB and less than or equal to 0 dB, frequency trackingMSE values are consistent and substantially constant at approximately200 Hz, again indicating (as shown and described above with reference toFIGS. 4A and 4B) that the systems and methods shown and described abovewith reference to FIGS. 1-3 are implementable with substantially similarbenefits in operation of the exemplary implementation on hardware andprocessing architectures having varying SNRs of greater than or equal to0 and less than or equal to 20 depending on particular applications ofsignal processing system 100.

FIG. 7A is a graphical representation (e.g., graph 700) of operation ofthe signal processing system 100 shown in FIG. 1 depicting values forcoefficient α₁ determined during pre-training versus window size withmultiple SNRs. FIG. 7B is a graphical representation (e.g., graph 702)of operation of the signal processing system 100 shown in FIG. 1depicting values for coefficient α₂ determined during pre-trainingversus window size with multiple SNRs. FIG. 7C is a graphicalrepresentation (e.g., graph 704) of operation of the signal processingsystem 100 shown in FIG. 1 depicting values for coefficient α₃determined during pre-training versus window size with multiple SNRs.FIG. 7D is a graphical representation (e.g., graph 706) of operation ofthe signal processing system 100 shown in FIG. 1 depicting values forcoefficient β₁ determined during pre-training versus window size withmultiple SNRs. FIG. 7E is a graphical representation (e.g., graph 708)of operation of the signal processing system 100 shown in FIG. 1depicting values for coefficient β₂ determined during pre-trainingversus window size with multiple SNRs. FIG. 7F is a graphicalrepresentation (e.g., graph 710) of operation of the signal processingsystem 100 shown in FIG. 1 depicting values for coefficient β₃determined during pre-training versus window size with multiple SNRs.

In the exemplary implementation, graph 700 plots results for coefficientα₁ (y-axis) determined at nine different SNRs using the systems andmethods described above with reference to FIGS. 1-3. Results of α₁ arealso plotted in graph 700 over window sizes of approximately 100 toapproximately 1000 on the x-axis. Graph 700 includes a first plot 711 ofdetermined α₁ values at an SNR of 0 dB. Graph 700 also includes a secondplot 712 and a third plot 713 of determined α₁ values at SNRs of 5 dBand 10 dB, respectively. Graph 700 further includes a fourth plot 714and a fifth plot 715 of determined α₁ values at SNRs of 15 dB and 20 dB,respectively. Graph 700 also includes a sixth plot 716 and a seventhplot 717 of determined α₁ values at SNRs of 25 dB and 30 dB,respectively. Graph 700 further includes an eighth plot 718 and a ninthplot 719 of determined α₁ values at SNRs of 35 dB and 40 dB,respectively.

Also, in the exemplary implementation, between window sizes of about 100and 1000, all plots (711, 712, 713, 714, 715, 716, 717, 718, and 719) ofgraph 700 are substantially equal in graph 700 and substantiallyoverlap, indicating that determined values of α₁ exhibit a substantiallysimilar dependency relationship with respect to window size for allSNRs. The aforementioned dependency relationship indicates that thesystems and methods shown and described above with reference to FIGS.1-3 are implementable with substantially similar benefits in thepre-training process for determining α₁ during operation of theexemplary implementation on hardware and processing architectures havingvarying SNRs depending on particular applications of signal processingsystem 100.

Further, in the exemplary implementation, graph 702 plots results forcoefficient α₂ (y-axis) determined at nine different SNRs using thesystems and methods described above with reference to FIGS. 1-3. Resultsof α₂ are also plotted in graph 702 over window sizes of approximately100 to approximately 1000 on the x-axis. Graph 702 includes a tenth plot720 of determined α₂ values at an SNR of 0 dB. Graph 702 also includesan eleventh plot 721 and a twelfth plot 722 of determined α₂ values atSNRs of 5 dB and 10 dB, respectively. Graph 702 further includes athirteenth plot 723 and a fourteenth plot 724 of determined α₂ values atSNRs of 15 dB and 20 dB, respectively. Graph 702 also includes afifteenth plot 725 and a sixteenth plot 726 of determined α₂ values atSNRs of 25 dB and 30 dB, respectively. Graph 702 further includes aseventeenth plot 727 and an eighteenth plot 728 of determined a_(z)values at SNRs of 35 dB and 40 dB, respectively.

Furthermore, in the exemplary implementation, between window sizes ofabout 100 and 1000, all plots (720, 721, 722, 723, 724, 725, 726, 727,and 728) of graph 702 are substantially equal in graph 702 andsubstantially overlap, indicating that determined values of α₂ exhibit asubstantially similar dependency relationship with respect to windowsize for all SNRs. The aforementioned dependency relationship indicatesthat the systems and methods shown and described above with reference toFIGS. 1-3 are implementable with substantially similar benefits in thepre-training process for determining α₂ during operation of theexemplary implementation on hardware and processing architectures havingvarying SNRs depending on particular applications of signal processingsystem 100.

Moreover, in the exemplary implementation, graph 704 plots results forcoefficient α₃ (y-axis) determined at nine different SNRs using thesystems and methods described above with reference to FIGS. 1-3. Resultsof α₃ are also plotted in graph 704 over window sizes of approximately100 to approximately 1000 on the x-axis. Graph 704 includes a nineteenthplot 729 of determined α₃ values at an SNR of 0 dB. Graph 704 alsoincludes a twentieth plot 730 and a twenty-first plot 731 of determinedα₃ values at SNRs of 5 dB and 10 dB, respectively. Graph 704 furtherincludes a twenty-second plot 732 and a twenty-third plot 733 ofdetermined α₃ values at SNRs of 15 dB and 20 dB, respectively. Graph 704also includes a twenty-fourth plot 734 and a twenty-fifth plot 735 ofdetermined α₃ values at SNRs of 25 dB and 30 dB, respectively. Graph 704further includes a twenty-sixth plot 736 and a twenty-seventh plot 737of determined α₃ values at SNRs of 35 dB and 40 dB, respectively.

Also, in the exemplary implementation, between window sizes of about 400and 1000, all plots (729, 730, 731, 732, 733, 734, 735, 736, and 737) ofgraph 704 are substantially equal in graph 704 and substantiallyoverlap, indicating that determined values of α₃ exhibit a substantiallysimilar dependency relationship with respect to window size for allSNRs. At windows size values between 100 and 400, on the other hand, allplots (730, 731, 732, 733, 734, 735, 736, and 737) except for nineteenthplot 729 (for 0 dB) are substantially equal and overlapping, againindicating a substantially similar dependency relationship with respectto window size. For nineteenth plot 729, however, determined values ofα₃ for SNR 0 dB are up to 0.003 different for window sizes of 100 to400. The aforementioned dependency relationship indicates that thesystems and methods shown and described above with reference to FIGS.1-3 are implementable with substantially similar benefits in thepre-training process for determining α₃ during operation of theexemplary implementation on hardware and processing architectures havingSNRs ranging from 5 dB to 40 dB depending on particular applications ofsignal processing system 100.

Further, in the exemplary implementation, graph 706 plots results forcoefficient β₁ (y-axis) determined at nine different SNRs using thesystems and methods described above with reference to FIGS. 1-3. Resultsof β₁ are also plotted in graph 706 over window sizes of approximately100 to approximately 1000 on the x-axis. Graph 706 includes atwenty-eighth plot 738 of determined β₁ values at an SNR of 0 dB. Graph706 also includes a twenty-ninth plot 739 and a thirtieth plot 740 ofdetermined β₁ values at SNRs of 5 dB and 10 dB, respectively. Graph 706further includes a thirty-first plot 741 and a thirty-second plot 742 ofdetermined β₁ values at SNRs of 15 dB and 20 dB, respectively. Graph 706also includes a thirty-third plot 743 and a thirty-fourth plot 744 ofdetermined β₁ values at SNRs of 25 dB and 30 dB, respectively. Graph 706further includes a thirty-fifth plot 745 and a thirty-sixth plot 746 ofdetermined β₁ values at SNRs of 35 dB and 40 dB, respectively.

Furthermore, in the exemplary implementation, between window sizes ofabout 100 and 1000, all plots (738, 739, 740, 741, 742, 743, 744, 745,and 746) of graph 706 are substantially equal in graph 706 andsubstantially overlap, indicating that determined values of β₁ exhibit asubstantially similar dependency relationship with respect to windowsize for all SNRs. The aforementioned dependency relationship indicatesthat the systems and methods shown and described above with reference toFIGS. 1-3 are implementable with substantially similar benefits in thepre-training process for determining β₁ during operation of theexemplary implementation on hardware and processing architectures havingvarying SNRs depending on particular applications of signal processingsystem 100.

Moreover, in the exemplary implementation, graph 708 plots results forcoefficient β₂ (y-axis) determined at nine different SNRs using thesystems and methods described above with reference to FIGS. 1-3. Resultsof β₂ are also plotted in graph 708 over window sizes of approximately100 to approximately 1000 on the x-axis. Graph 708 includes athirty-seventh plot 747 of determined β₂ values at an SNR of 0 dB. Graph708 also includes a thirty-eighth plot 748 and a thirty-ninth plot 749of determined β₂ values at SNRs of 5 dB and 10 dB, respectively. Graph708 further includes a fortieth plot 750 and a forty-first plot 751 ofdetermined β₂ values at SNRs of 15 dB and 20 dB, respectively. Graph 708also includes a forty-second plot 752 and a forty-third plot 753 ofdetermined β₂ values at SNRs of 25 dB and 30 dB, respectively. Graph 708further includes a forty-fourth plot 754 and a forty-fifth plot 755 ofdetermined β₂ values at SNRs of 35 dB and 40 dB, respectively.

Also, in the exemplary implementation, plots (751, 752, 753, 754, and755) of graph 708 are substantially equal in graph 708 and substantiallyoverlap, indicating that determined values of β₂ exhibit a substantiallysimilar dependency relationship with respect to window size for SNRs of20 dB to 40 dB between window sizes of about 100 and 1000. For lower SNRplots (747, 748, 749, and 750) for window sizes 100 to 1000, however,determined values of β₂ exhibit significant variation from plots (751,752, 753, 754, and 755) by up to about 10. The aforementioned dependencyrelationship indicates that the systems and methods shown and describedabove with reference to FIGS. 1-3 are implementable with substantiallysimilar benefits in the pre-training process for determining β₂ duringoperation of the exemplary implementation on hardware and processingarchitectures having SNRs ranging from 20 dB to 40 dB depending onparticular applications of signal processing system 100.

Further, in the exemplary implementation, graph 710 plots results forcoefficient β₃ (y-axis) determined at nine different SNRs using thesystems and methods described above with reference to FIGS. 1-3. Resultsof β₃ are also plotted in graph 710 over window sizes of approximately100 to approximately 1000 on the x-axis. Graph 710 includes aforty-sixth plot 756 of determined β₃ values at an SNR of 0 dB. Graph710 also includes a forty-seventh plot 757 and a forty-eighth plot 758of determined β₃ values at SNRs of 5 dB and 10 dB, respectively. Graph710 further includes a forty-ninth plot 759 and a fiftieth plot 760 ofdetermined β₃ values at SNRs of 15 dB and 20 dB, respectively. Graph 710also includes a fifty-first plot 761 and a fifty-second plot 762 ofdetermined β₃ values at SNRs of 25 dB and 30 dB, respectively. Graph 710further includes a fifty-third plot 763 and a fifty-fourth plot 764 ofdetermined β₃ values at SNRs of 35 dB and 40 dB, respectively.

Furthermore, in the exemplary implementation, between window sizes ofabout 100 and 1000, all plots (756, 757, 758, 759, 760, 761, 762, 763,and 764) of graph 710 are substantially equal in graph 710 andsubstantially overlap, indicating that determined values of β₃ exhibit asubstantially similar dependency relationship with respect to windowsize for all SNRs. The aforementioned dependency relationship indicatesthat the systems and methods shown and described above with reference toFIGS. 1-3 are implementable with substantially similar benefits in thepre-training process for determining β₃ during operation of theexemplary implementation on hardware and processing architectures havingvarying SNRs depending on particular applications of signal processingsystem 100.

FIG. 8A is a graphical representation (e.g., graph 800) of operation ofthe signal processing system 100 shown in FIG. 1 depicting MSE resultsfor Δf determined during frequency tracking versus window size withmultiple SNRs. FIG. 8B is a graphical representation (e.g., graph 802)of operation of the signal processing system 100 shown in FIG. 1depicting MSE results for Δw determined during frequency tracking versuswindow size with multiple SNRs. In the exemplary implementation, graph800 plots results for MSE of Δf (y-axis) determined for nine differentSNRs using the systems and methods described above with reference toFIGS. 1-3. Results of MSE of Δf are also plotted in graph 800 overwindow sizes of 100 to about 1050 on the x-axis. Graph 800 includes afirst plot 804 of determined MSE of Δf values at an SNR of 0 dB. Graph800 also includes a second plot 806 and a third plot 808 of determinedMSE of Δf values at SNRs of 5 dB and 10 dB, respectively. Graph 800further includes a fourth plot 810 and a fifth plot 812 of determinedMSE of Δf values at SNRs of 15 dB and 20 dB, respectively. Graph 800also includes a sixth plot 814 and a seventh plot 816 of determined MSEof Δf values at SNRs of 25 dB and 30 dB, respectively. Graph 800 furtherincludes an eighth plot 818 and a ninth plot 820 of determined MSE of Δfvalues at SNRs of 30 dB and 35 dB, respectively. Also, in the exemplaryimplementation, all plots (804, 806, 808, 810, 812, 814, 816, 818, and820) of graph 800 are substantially equal in graph 800 and substantiallyoverlap, indicating that determined values of MSE of Δf exhibit asubstantially similar dependency relationship with respect to windowsize for all SNRs. The aforementioned dependency relationship indicatesthat the systems and methods shown and described above with reference toFIGS. 1-3 are implementable with substantially similar benefits inoperation of the exemplary implementation on hardware and processingarchitectures having varying SNRs depending on particular applicationsof signal processing system 100.

Further, in the exemplary implementation, graph 802 plots results forMSE of Δw (y-axis) determined for nine different SNRs using the systemsand methods described above with reference to FIGS. 1-3. Results of MSEof Δw are also plotted in graph 802 over window sizes of 100 to about1050 on the x-axis. Graph 802 includes a tenth plot 822 of determinedMSE of Δw values at an SNR of 0 dB. Graph 802 also includes an eleventhplot 824 and a twelfth plot 826 of determined MSE of Δw values at SNRsof 5 dB and 10 dB, respectively. Graph 802 further includes a thirteenthplot 828 and a fourteenth plot 830 of determined MSE of Δw values atSNRs of 15 dB and 20 dB, respectively. Graph 802 also includes afifteenth plot 832 and a sixteenth plot 834 of determined MSE of Δwvalues at SNRs of 25 dB and 30 dB, respectively. Graph 802 furtherincludes a seventeenth plot 836 and an eighteenth plot 838 of determinedMSE of Δw values at SNRs of 30 dB and 35 dB, respectively. Also, in theexemplary implementation, all plots (822, 824, 826, 828, 830, 832, 834,836, and 838) of graph 802 are substantially equal in graph 802 andsubstantially overlap, indicating that determined values of MSE of Δwexhibit a substantially similar dependency relationship with respect towindow size for all SNRs. The aforementioned dependency relationshipindicates that the systems and methods shown and described above withreference to FIGS. 1-3 are implementable with substantially similarbenefits in operation of the exemplary implementation on hardware andprocessing architectures having varying SNRs depending on particularapplications of signal processing system 100.

FIG. 9 is a flowchart of an exemplary method 900 for generating PDWsusing BSS that may be used with the signal processing system 100 shownin FIG. 1. In the exemplary implementation, method 900 includesfiltering 902, at the plurality of BSS modules 120 of the signal dataprocessor 101, signals (e.g., denoised signals 124 and state energysignals 126) derived from the plurality of time-varying signals (e.g.,first 114 and second 116 radar signals). Method 900 also includestransmitting 904 at least one blind source separated signal 129 from theplurality of BSS modules 120 to the PDW generation module 128communicatively coupled to filtering subsystem 207. Method 900 furtherincludes generating 906, using the PDW generation module 128 and basedon the at least one blind source separated signal 129, at least one PDWparameter vector signal 138 containing the frequency data. Method 900also includes updating 908, upon generating the at least one PDWparameter vector signal 138, and based thereupon, at least one of avalue of a and a value of f for each filter module of the plurality offilter modules (e.g., low filter module 222, main filter module 224, andhigh filter module 226).

The above-described systems and methods for PDW generation using blindsource separation enable enhanced accuracy of PDW parameter estimationswithout relying on fixed bandwidth channels. The above-describedimplementations also facilitate faster and more efficient PDW generationusing less complex processing architectures relative to known fixedbandwidth channel-based systems. The above-described implementationsfurther enable reduction of size, weight, and cost of high performancePDW signal processing systems and methods. The above-described systemsand methods for PDW generation using blind source separation alsoprovide continuous high speed generation of high signal quality PDWvectors suitable for improved deinterleaving methods.

An exemplary technical effect of the above-described systems and methodsfor PDW generation using blind source separation includes at least oneof the following: (a) enhancing accuracy of PDW parameter estimationswithout relying on fixed bandwidth channels; (b) increasing speed andefficiency of PDW generation using less complex processing architecturesrelative to known systems; (c) reducing size, weight, and cost of highperformance PDW signal processing systems; and (d) providing continuoushigh speed generation of high signal quality PDW vectors suitable forimproved deinterleaving methods.

Although specific features of various implementations of the disclosuremay be shown in some drawings and not in others, this is for convenienceonly. In accordance with the principles of the disclosure, any featureof a drawing may be referenced and/or claimed in combination with anyfeature of any other drawing.

Some implementations involve the use of one or more electronic orcomputing devices. Such devices typically include a processor,processing device, or controller, such as a general purpose centralprocessing unit (CPU), a graphics processing unit (GPU), amicrocontroller, a reduced instruction set computer (RISC) processor, anASIC, a programmable logic circuit (PLC), an FPGA, a DSP device, and/orany other circuit or processing device capable of executing thefunctions described herein. The methods described herein may be encodedas executable instructions embodied in a computer-readable medium,including, without limitation, a storage device and/or a memory device.Such instructions, when executed by a processing device, cause theprocessing device to perform at least a portion of the methods describedherein. The above examples are exemplary only, and thus are not intendedto limit in any way the definition and/or meaning of the term processorand processing device.

This written description uses examples to disclose the implementations,including the best mode, and also to enable any person skilled in theart to practice the implementations, including making and using anydevices or systems and performing any incorporated methods. Thepatentable scope of the disclosure is defined by the claims, and mayinclude other examples that occur to those skilled in the art. Suchother examples are intended to be within the scope of the claims if theyhave structural elements that do not differ from the literal language ofthe claims, or if they include equivalent structural elements withinsubstantial differences from the literal language of the claims.

What is claimed is:
 1. A method for generating pulse descriptor words(“PDWs”) including at least one of frequency data and bandwidth data,from a plurality of time-varying signals received by a sensorcommunicatively coupled to a signal data processor, said methodcomprising: filtering, at a plurality of blind source separation (“BSS”)modules of the signal data processor, signals derived from the pluralityof time-varying signals, each BSS module of the plurality of BSS modulesincluding a filtering subsystem having a plurality of filter modules,wherein each filter module of the plurality of filter modules has afrequency filter coefficient (“α”) and is parameterized by a centerfrequency (“f”); transmitting at least one blind source separated signalfrom the plurality of BSS modules to a PDW generation modulecommunicatively coupled to the filtering subsystem; generating, usingthe PDW generation module and based on the at least one blind sourceseparated signal, at least one PDW parameter vector signal containingthe frequency data; and updating, upon generating the at least one PDWparameter vector signal, and based thereupon, at least one of a value ofa and a value of f for each filter module of the plurality of filtermodules.
 2. The method in accordance with claim 1 further comprisingstoring, in a memory communicatively coupled to the signal dataprocessor, at least one of an updated value of α and an updated value off, wherein updating at least one of the value of α and the value of fcomprises transmitting at least one of the updated value of α and theupdated value of f to the each filter module to facilitate tracking thefrequency data for the plurality of time-varying signals.
 3. The methodin accordance with claim 1 further comprising storing, in a memorycommunicatively coupled to the signal data processor, at least one of aninitial value of α and an initial value of f.
 4. The method inaccordance with claim 1, wherein filtering signals comprises receivingdenoised signals and state energy signals from at least one signaldenoising module, said method further comprising determining a value ofsignal energy of the signals to facilitate tracking at least one of thefrequency data and the bandwidth data for the plurality of time-varyingsignals.
 5. The method in accordance with claim 1, wherein filtering thesignals comprises using at least one filter module of the plurality offilter modules having a bandwidth filter coefficient (“β”) and furtherparameterized by a bandwidth (“w”), and wherein said method furthercomprises updating at least one of a value of β and a value of w of theat least one filter module.
 6. The method in accordance with claim 5further comprising storing, in a memory communicatively coupled to thesignal data processor, at least one of an updated value of β and anupdated value of w, wherein updating at least one of the value of β andthe value of w comprises transmitting at least one of the updated valueof β and the updated value of w to the each filter module to facilitatetracking the bandwidth data for the plurality of time-varying signals.7. The method in accordance with claim 5 further comprising storing, ina memory communicatively coupled to the signal data processor, at leastone of an initial value of β and an initial value of w.
 8. The method inaccordance with claim 1 further comprising outputting the at least onePDW parameter vector signal from the PDW generation module to acomputing device communicatively coupled to the signal data processor.9. The method in accordance with claim 8 further comprising directingmovement of a vehicle based on the at least one PDW parameter vectorsignal.
 10. The method in accordance with claim 8 further comprisingdisplaying at least one of the at least one PDW parameter vector signaland information derived therefrom on a display.
 11. A system forprocessing a plurality of time-varying signals to generate at least onepulse descriptor word (“PDW”) including at least one of frequency dataand bandwidth data, said system comprising: a sensor configured toreceive the at least one time-varying signal; a signal data processorcommunicatively coupled to said sensor and comprising: a plurality ofblind source separation (“BSS”) modules, each BSS module of saidplurality of BSS modules comprising a filtering subsystem comprising aplurality of filter modules, wherein each filter module of saidplurality of filter modules has a frequency filter coefficient (“α”) andis parameterized by a center frequency (“f”); and a PDW generationmodule communicatively coupled to said filtering subsystem, saidplurality of BSS modules configured to filter signals derived from theplurality of time-varying signals and transmit at least one blind sourceseparated signal to said PDW generation module, said PDW generationmodule configured to generate, based on the at least one blind sourceseparated signal, at least one PDW parameter vector signal containingthe frequency data to facilitate updating, substantially simultaneouslywith generating the at least one PDW parameter vector signal, and basedthereupon, at least one of a value of α and a value of f for each filtermodule of said plurality of filter modules.
 12. The system in accordancewith claim 11 further comprising a memory configured to store at leastone of an updated value of α and an updated value of f, wherein saideach filter module is configured to receive at least one of the updatedvalue of α and the updated value of f to facilitate tracking thefrequency data for the plurality of time-varying signals.
 13. The systemin accordance with claim 11 further comprising at least one signaldenoising module configured to generate denoised signals and stateenergy signals derived from the plurality of time-varying signals, saidsystem configured to determine a value of signal energy of the signalsto facilitate tracking at least one of the frequency data and thebandwidth data for the plurality of time-varying signals.
 14. The systemin accordance with claim 11, wherein at least one filter module of saidplurality of filter modules has a bandwidth filter coefficient (“β”) andis further parameterized by a bandwidth (“w”), the at least one PDWparameter vector signal further containing the bandwidth data tofacilitate updating, substantially simultaneously with generating the atleast one PDW parameter vector signal, and based thereupon, at least oneof a value of β and a value of w of said at least one filter module. 15.The system in accordance with claim 14 further comprising a memoryconfigured to store at least one of an updated value of β and an updatedvalue of w, wherein said at least one filter module is configured toreceive at least one of the updated value of β and the updated value ofw to facilitate tracking the bandwidth data for the plurality oftime-varying signals.
 16. The system in accordance with claim 11 furthercomprising a computing device communicatively coupled to said signaldata processor and communicatively coupled to said memory, saidcomputing device configured to: receive the at least one PDW parametervector signal from said PDW generation module; deinterleave the at leastone PDW parameter vector signal; and transmit at least one frequencyword signal to said signal data processing to further facilitateupdating, substantially simultaneously with generating the at least onePDW parameter vector signal, and based thereupon, at least one of thevalue of α and the value of f for said each filter module.
 17. Thesystem in accordance with claim 16 further comprising a vehicle incommunication with said computing device, said system configured todirect movement of said vehicle based on the at least one PDW parametervector signal.
 18. The system in accordance with claim 16 furthercomprising a display communicatively coupled to said computing device,said computing device configured to display at least one of the at leastone PDW parameter vector signal and information derived therefrom onsaid display.
 19. A signal data processor for processing a plurality oftime-varying signals to generate at least one pulse descriptor word(“PDW”) including at least one of frequency data and bandwidth data,said signal data processor comprising: a plurality of blind sourceseparation (“BSS”) modules, each BSS module of said plurality of BSSmodules comprising a filtering subsystem comprising a plurality offilter modules, wherein each filter module of said plurality of filtermodules has a frequency filter coefficient (“α”) and is parameterized bya center frequency (“β”); and a PDW generation module communicativelycoupled to said filtering subsystem, said plurality of BSS modulesconfigured to filter signals derived from the plurality of time-varyingsignals and transmit at least one blind source separated signal to saidPDW generation module, said PDW generation module configured togenerate, based on the at least one blind source separated signal, atleast one PDW parameter vector signal containing the frequency data tofacilitate updating, substantially simultaneously with generating the atleast one PDW parameter vector signal, and based thereupon, at least oneof a value of α and a value of f for each filter module of saidplurality of filter modules.
 20. The signal data processor in accordancewith claim 19 further comprising at least one signal denoising moduleconfigured to generate denoised signals and state energy signals derivedfrom the plurality of time-varying signals, said signal processingsystem configured to determine a value of signal energy of the signalsto facilitate tracking at least one of the frequency data and thebandwidth data for the plurality of time-varying signals.
 21. The signaldata processor in accordance with claim 19, wherein at least one filtermodule of said plurality of filter modules has a bandwidth filtercoefficient (“β”) and is further parameterized by a bandwidth (“w”), theat least one PDW parameter vector signal further containing thebandwidth data to facilitate updating, substantially simultaneously withgenerating the at least one PDW parameter vector signal, and basedthereupon, at least one of a value of β and a value of w of said atleast one filter module.